(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.4' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     17479,        594]
NotebookOptionsPosition[     14085,        494]
NotebookOutlinePosition[     16355,        552]
CellTagsIndexPosition[     16270,        547]
WindowTitle->FCLoopBasisExtract
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[GridBox[{
   {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[Cell[BoxData[
     ActionMenuBox[
      FrameBox[
       InterpretationBox[Cell[TextData[{
         "URL",
         StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
          StripOnInput->False]
        }]],
        TextCell[
         Row[{"URL", 
           Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
       StripOnInput->False], {"\<\"FeynCalc/ref/FCLoopBasisExtract\"\>":>
      None, "\<\"Copy Wolfram Documentation Center URL\"\>":>
      Module[{DocumentationSearch`Private`nb$}, 
       DocumentationSearch`Private`nb$ = NotebookPut[
          Notebook[{
            Cell["FeynCalc/ref/FCLoopBasisExtract"]}, Visible -> False]]; 
       SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
       FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
       NotebookClose[DocumentationSearch`Private`nb$]; Null], 
      Delimiter, "\<\"Copy web URL\"\>":>
      Module[{DocumentationSearch`Private`nb$}, 
       DocumentationSearch`Private`nb$ = NotebookPut[
          Notebook[{
            Cell[
             BoxData[
              MakeBoxes[
               Hyperlink[
               "http://reference.wolfram.com/language/FeynCalc/ref/\
FCLoopBasisExtract.html"], StandardForm]], "Input", TextClipboardType -> 
             "PlainText"]}, Visible -> False]]; 
       SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
       FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
       NotebookClose[DocumentationSearch`Private`nb$]; 
       Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{
        NotebookLocate[{
          URL[
           StringJoin[
            If[
             TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$105975], 
             "http://reference.wolfram.com/system-modeler/", 
             "http://reference.wolfram.com/language/"], 
            "FeynCalc/ref/FCLoopBasisExtract", ".html"]], None}]}]},
      Appearance->None,
      MenuAppearance->Automatic,
      MenuStyle->"URLMenu"]],
     LineSpacing->{1.4, 0}]], "AnchorBar"]}
  }]], "AnchorBarGrid",
 GridBoxOptions->{GridBoxItemSize->{"Columns" -> {
     Scaled[0.65], {
      Scaled[0.34]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
   "RowsIndexed" -> {}}},
 CellID->1],

Cell[TextData[{
 Cell["FCLoopBasisExtract", "ObjectName"],
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{8, 0}],
    CacheGraphics->False],
   Spacer[8]]]],
 Cell[BoxData[""], "ObjectNameTranslation"]
}], "ObjectNameGrid"],

Cell[CellGroupData[{

Cell[BoxData[GridBox[{
   {"", Cell[TextData[{
     Cell[BoxData[
      RowBox[{"FCLoopBasisExtract", "[", 
       RowBox[{"int", ",", 
        RowBox[{"{", 
         RowBox[{"q1", ",", "q2", ",", "..."}], "}"}]}], "]"}]], 
      "InlineFormula"],
     " \[LineSeparator] is an auxiliary function that extracts the scalar \
products that form the basis of the loop integral in int. It needs to know \
the loop momenta on which the integral depends and the dimensions of the \
momenta that may occur in the integral."
    }]]}
  }]], "Usage",
 GridBoxOptions->{
 GridBoxBackground->{
  "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, 
   "RowsIndexed" -> {}}},
 CellID->982511436],

Cell[CellGroupData[{

Cell[TextData[Cell[BoxData[
 ButtonBox[Cell[TextData[{
   Cell[BoxData[
    InterpretationBox[
     StyleBox[
      GraphicsBox[{},
       BaselinePosition->Baseline,
       ImageSize->{6, 0}],
      CacheGraphics->False],
     Spacer[6]]]],
   "Details"
  }], "NotesFrameText"],
  Appearance->{Automatic, None},
  BaseStyle->None,
  ButtonFunction:>(FrontEndExecute[{
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], All, ButtonCell], 
     FrontEndToken["OpenCloseGroup"], 
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], After, CellContents]}]& ),
  Evaluator->None,
  Method->"Preemptive"]]]], "NotesSection",
 WholeCellGroupOpener->True,
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->706770986],

Cell["", "SectionHeaderSpacer"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Options", "[", "FCLoopBasisExtract", "]"}]], "Input",
 CellLabel->"In[20]:=",
 CellID->976561677],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", 
    RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", 
    RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", 
    RowBox[{"FCTopology", "\[Rule]", "False"}], ",", 
    RowBox[{"SetDimensions", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"3", ",", "4", ",", "D", ",", 
       RowBox[{"D", "-", "1"}]}], "}"}]}]}], "}"}], 
  TraditionalForm]], "Output",
 ImageSize->{484, 35},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[20]=",
 CellID->1988549580]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "PrimaryExamplesSection",
 WholeCellGroupOpener->True,
 CellTags->"PrimaryExamplesSection",
 CellID->478631788],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "ExampleSection", "ExampleSection",
 WholeCellGroupOpener->True,
 CellID->1731678010],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"SPD", "[", 
   RowBox[{"q", ",", "p"}], "]"}], " ", 
  RowBox[{"SFAD", "[", 
   RowBox[{"q", ",", 
    RowBox[{"q", "-", "p"}], ",", 
    RowBox[{"q", "-", "p"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{"FCLoopBasisExtract", "[", 
  RowBox[{"%", ",", 
   RowBox[{"{", "q", "}"}], ",", 
   RowBox[{"SetDimensions", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"4", ",", "D"}], "}"}]}]}], "]"}]}], "Input",
 CellLabel->"In[1]:=",
 CellID->1087542221],

Cell[BoxData[
 FormBox[
  FractionBox[
   FormBox[
    RowBox[{
     FormBox[
      FormBox["p",
       TraditionalForm],
      TraditionalForm], 
     FormBox["\<\"\[CenterDot]\"\>",
      TraditionalForm], 
     FormBox[
      FormBox["q",
       TraditionalForm],
      TraditionalForm]}],
    TraditionalForm], 
   RowBox[{
    TemplateBox[{"\"(\"",SuperscriptBox[
       FormBox[
        FormBox["q", TraditionalForm], TraditionalForm], 2],"\"+\"",
      RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""},
     "RowDefault"], ".", 
    SuperscriptBox[
     TemplateBox[{"\"(\"",RowBox[{
         SuperscriptBox[
          RowBox[{
            FormBox["\"(\"", TraditionalForm], 
            FormBox[
             FormBox[
              RowBox[{
                FormBox["q", TraditionalForm], "-", 
                FormBox["p", TraditionalForm]}], TraditionalForm], 
             TraditionalForm], 
            FormBox["\")\"", TraditionalForm]}], 2]}],"\"+\"",
       RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""},
      "RowDefault"], "2"]}]], TraditionalForm]], "Output",
 ImageSize->{189, 36},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[1]=",
 CellID->1913056698],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{
       FormBox[
        FormBox["p",
         TraditionalForm],
        TraditionalForm], 
       FormBox["\<\"\[CenterDot]\"\>",
        TraditionalForm], 
       FormBox[
        FormBox["q",
         TraditionalForm],
        TraditionalForm]}], ",", 
      SuperscriptBox[
       FormBox[
        FormBox["q",
         TraditionalForm],
        TraditionalForm], "2"], ",", 
      RowBox[{
       RowBox[{"-", 
        RowBox[{"2", " ", 
         RowBox[{"(", 
          RowBox[{
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["\<\"\[CenterDot]\"\>",
            TraditionalForm], 
           FormBox[
            FormBox["q",
             TraditionalForm],
            TraditionalForm]}], ")"}]}]}], "+", 
       SuperscriptBox[
        FormBox[
         FormBox["p",
          TraditionalForm],
         TraditionalForm], "2"], "+", 
       SuperscriptBox[
        FormBox[
         FormBox["q",
          TraditionalForm],
         TraditionalForm], "2"]}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{
       FormBox[
        FormBox["p",
         TraditionalForm],
        TraditionalForm], 
       FormBox["\<\"\[CenterDot]\"\>",
        TraditionalForm], 
       FormBox[
        FormBox["q",
         TraditionalForm],
        TraditionalForm]}], ",", 
      SuperscriptBox[
       FormBox[
        FormBox["q",
         TraditionalForm],
        TraditionalForm], "2"]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "1"}], ",", "1", ",", "2"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{
       FormBox[
        FormBox["p",
         TraditionalForm],
        TraditionalForm], 
       FormBox["\<\"\[CenterDot]\"\>",
        TraditionalForm], 
       FormBox[
        FormBox["q",
         TraditionalForm],
        TraditionalForm]}], ",", 
      FormBox[
       FractionBox["1", 
        TemplateBox[{"\"(\"",SuperscriptBox[
           FormBox[
            FormBox["q", TraditionalForm], TraditionalForm], 2],"\"+\"",
          RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""},
         "RowDefault"]],
       TraditionalForm], ",", 
      FormBox[
       FractionBox["1", 
        TemplateBox[{"\"(\"",RowBox[{
            SuperscriptBox[
             RowBox[{
               FormBox["\"(\"", TraditionalForm], 
               FormBox[
                FormBox[
                 RowBox[{
                   FormBox["q", TraditionalForm], "-", 
                   FormBox["p", TraditionalForm]}], TraditionalForm], 
                TraditionalForm], 
               FormBox["\")\"", TraditionalForm]}], 2]}],"\"+\"",
          RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""},
         "RowDefault"]],
       TraditionalForm]}], "}"}]}], "}"}], TraditionalForm]], "Output",
 ImageSize->{341, 70},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[1]=",
 CellID->336549085]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"SFAD", "[", "p1", "]"}], "\[IndentingNewLine]", 
 RowBox[{"FCLoopBasisExtract", "[", 
  RowBox[{"%", ",", 
   RowBox[{"{", 
    RowBox[{"p1", ",", "p2", ",", "p3"}], "}"}], ",", 
   RowBox[{"FCTopology", "\[Rule]", "True"}], ",", 
   RowBox[{"FCE", "\[Rule]", "True"}]}], "]"}]}], "Input",
 CellLabel->"In[2]:=",
 CellID->280018364],

Cell[BoxData[
 FormBox[
  FractionBox["1", 
   TemplateBox[{"\"(\"",SuperscriptBox[
      FormBox[
       FormBox["p1", TraditionalForm], TraditionalForm], 2],"\"+\"",
     RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""},
    "RowDefault"]], TraditionalForm]], "Output",
 ImageSize->{72, 40},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[2]=",
 CellID->5648788],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{"{", 
     FormBox[
      SuperscriptBox[
       FormBox[
        FormBox["p1",
         TraditionalForm],
        TraditionalForm], "2"],
      TraditionalForm], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      FormBox[
       SuperscriptBox[
        FormBox[
         FormBox["p1",
          TraditionalForm],
         TraditionalForm], "2"],
       TraditionalForm], ",", 
      FormBox[
       RowBox[{
        FormBox[
         FormBox["p1",
          TraditionalForm],
         TraditionalForm], 
        FormBox["\<\"\[CenterDot]\"\>",
         TraditionalForm], 
        FormBox[
         FormBox["p2",
          TraditionalForm],
         TraditionalForm]}],
       TraditionalForm], ",", 
      FormBox[
       RowBox[{
        FormBox[
         FormBox["p1",
          TraditionalForm],
         TraditionalForm], 
        FormBox["\<\"\[CenterDot]\"\>",
         TraditionalForm], 
        FormBox[
         FormBox["p3",
          TraditionalForm],
         TraditionalForm]}],
       TraditionalForm], ",", 
      FormBox[
       SuperscriptBox[
        FormBox[
         FormBox["p2",
          TraditionalForm],
         TraditionalForm], "2"],
       TraditionalForm], ",", 
      FormBox[
       RowBox[{
        FormBox[
         FormBox["p2",
          TraditionalForm],
         TraditionalForm], 
        FormBox["\<\"\[CenterDot]\"\>",
         TraditionalForm], 
        FormBox[
         FormBox["p3",
          TraditionalForm],
         TraditionalForm]}],
       TraditionalForm], ",", 
      FormBox[
       SuperscriptBox[
        FormBox[
         FormBox["p3",
          TraditionalForm],
         TraditionalForm], "2"],
       TraditionalForm]}], "}"}], ",", 
    RowBox[{"{", "1", "}"}], ",", 
    RowBox[{"{", 
     FormBox[
      FractionBox["1", 
       TemplateBox[{"\"(\"",SuperscriptBox[
          FormBox[
           FormBox["p1", TraditionalForm], TraditionalForm], 2],"\"+\"",
         RowBox[{"\[ImaginaryI]", " ", "\"\[Eta]\""}],"\")\""},
        "RowDefault"]],
      TraditionalForm], "}"}]}], "}"}], TraditionalForm]], "Output",
 ImageSize->{438, 40},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[2]=",
 CellID->1391901442]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell[" ", "FooterCell"]
},
Saveable->False,
ScreenStyleEnvironment->"Working",
WindowSize->{725, 750},
WindowMargins->{{-10, Automatic}, {Automatic, -8}},
WindowTitle->"FCLoopBasisExtract",
TaggingRules->{
 "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> 
  GridBox[{{
      RowBox[{
        ButtonBox[
        "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", 
         BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> 
    Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> 
  None, "RootCaptions" -> "", 
  "Metadata" -> {
   "built" -> "{2020, 6, 20, 19, 5, 33.888997}", 
    "history" -> {"9.3", "", "", ""}, "context" -> "FeynCalc`", 
    "keywords" -> {}, "specialkeywords" -> {}, 
    "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> 
    "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> 
    "None", "summary" -> 
    "FCLoopBasisExtract[int, {q1, q2, ...}] is an auxiliary function that \
extracts the scalar products that form the basis of the loop integral in int. \
It needs to know the loop momenta on which the integral depends and the \
dimensions of the momenta that may occur in the integral.", "synonyms" -> {}, 
    "tabletags" -> {}, "title" -> "FCLoopBasisExtract", "titlemodifier" -> "",
     "windowtitle" -> "FCLoopBasisExtract", "type" -> "Symbol", "uri" -> 
    "FeynCalc/ref/FCLoopBasisExtract"}, "SearchTextTranslated" -> ""},
CellContext->"Global`",
FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], 
   Cell[
    StyleData["Input"], CellContext -> "Global`"], 
   Cell[
    StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, 
  FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", 
  StyleDefinitions -> "Default.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "PrimaryExamplesSection"->{
  Cell[5532, 172, 387, 15, 31, "PrimaryExamplesSection",
   CellTags->"PrimaryExamplesSection",
   CellID->478631788]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"PrimaryExamplesSection", 16127, 540}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[590, 21, 2314, 53, 53, "AnchorBarGrid",
 CellID->1],
Cell[2907, 76, 295, 11, 45, "ObjectNameGrid"],
Cell[CellGroupData[{
Cell[3227, 91, 698, 18, 119, "Usage",
 CellID->982511436],
Cell[CellGroupData[{
Cell[3950, 113, 738, 24, 31, "NotesSection",
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->706770986],
Cell[4691, 139, 31, 0, 70, "SectionHeaderSpacer"],
Cell[CellGroupData[{
Cell[4747, 143, 121, 3, 70, "Input",
 CellID->976561677],
Cell[4871, 148, 600, 17, 56, "Output",
 CellID->1988549580]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[5532, 172, 387, 15, 31, "PrimaryExamplesSection",
 CellTags->"PrimaryExamplesSection",
 CellID->478631788],
Cell[CellGroupData[{
Cell[5944, 191, 196, 6, 26, "ExampleSection",
 CellID->1731678010],
Cell[CellGroupData[{
Cell[6165, 201, 486, 15, 45, "Input",
 CellID->1087542221],
Cell[6654, 218, 1222, 40, 57, "Output",
 CellID->1913056698],
Cell[7879, 260, 3061, 109, 91, "Output",
 CellID->336549085]
}, Open  ]],
Cell[CellGroupData[{
Cell[10977, 374, 357, 9, 45, "Input",
 CellID->280018364],
Cell[11337, 385, 404, 12, 61, "Output",
 CellID->5648788],
Cell[11744, 399, 2275, 88, 61, "Output",
 CellID->1391901442]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[14058, 492, 23, 0, 41, "FooterCell"]
}
]
*)

(* End of internal cache information *)

